Solve y=2sinx^2

$$y = 2 \sin x ^ { 2 }$$

Solve for x (complex solution)

$$x=\left(-1\right)\left(\left(-i\right)\ln(\frac{1}{2}iy+\left(-\frac{1}{2}i\right)\left(y^{2}-4\right)^{\frac{1}{2}})+2\pi n_{1}\right)^{\frac{1}{2}}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\left(\left(-i\right)\ln(\frac{1}{2}iy+\left(-\frac{1}{2}i\right)\left(y^{2}-4\right)^{\frac{1}{2}})+2\pi n_{1}\right)^{\frac{1}{2}}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\left(-1\right)\left(\left(-i\right)\ln(\frac{1}{2}iy+\frac{1}{2}i\left(y^{2}-4\right)^{\frac{1}{2}})+2\pi n_{5}\right)^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}$$

$$x=\left(\left(-i\right)\ln(\frac{1}{2}iy+\frac{1}{2}i\left(y^{2}-4\right)^{\frac{1}{2}})+2\pi n_{5}\right)^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}$$

Solve for x

$$\left\{\begin{matrix}\\x=-\sqrt{\arcsin(\frac{y}{2})+2\pi n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }\left(n_{1}\geq 1\text{ and }|y|\leq 2\right)\text{ or }\left(n_{1}>-1\text{ and }y\leq 2\text{ and }y\geq 0\right)\text{; }x=\sqrt{\arcsin(\frac{y}{2})+2\pi n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }\left(n_{1}\geq 1\text{ and }|y|\leq 2\right)\text{ or }\left(n_{1}>-1\text{ and }y\leq 2\text{ and }y\geq 0\right)\text{, }&\text{unconditionally}\\x=\sqrt{-\arcsin(\frac{y}{2})+2\pi n_{2}+\pi }\text{, }n_{2}\in \mathrm{Z}\text{, }n_{2}>-1\text{; }x=-\sqrt{-\arcsin(\frac{y}{2})+2\pi n_{2}+\pi }\text{, }n_{2}\in \mathrm{Z}\text{, }n_{2}>-1\text{, }&|y|\leq 2\end{matrix}\right.$$

Solve for y

$$y=2\sin(x^{2})$$